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Coprime Count Modulo 8

Let $ n $ be the number of integers $ m $ in the range $ 1\le m\le 8 $ such that $ \text{gcd}(m,8)=1 $. What is the remainder when $ 3^n $ is divided by $ 8 $?

1
2
3
+
4
5
6
-
7
8
9
$\frac{a}{b}$
.
0
=
%

$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

$($
$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$